Warning

This is A PREVIEW for NEST 3.0 and NOT an OFFICIAL RELEASE! Some functionality may not be available and information may be incomplete!

# noise_generator – Device to generate Gaussian white noise current¶

## Description¶

This device can be used to inject a Gaussian “white” noise current into a node.

The current is not really white, but a piecewise constant current with Gaussian distributed amplitude. The current changes at intervals of dt. dt must be a multiple of the simulation step size, the default is 1.0 ms, corresponding to a 1 kHz cut-off. Additionally a second sinusodial modulated term can be added to the standard deviation of the noise.

The current generated is given by

$I(t) = mean + std * N_j \text{ for } t_0 + j dt \leq t < t_0 + (j-1) dt$

where $$N_j$$ are Gaussian random numbers with unit standard deviation and $$t_0$$ is the device onset time. If the modulation is added the current is given by

$\begin{split}I(t) = mean + \sqrt(std^2 + std_{mod}^2 * \sin(\omega * t + phase)) * N_j \\ \text{ for } t_0 + j dt \leq t < t_0 + (j-1) dt\end{split}$

For a detailed discussion of the properties of the noise generator, please see noise_generator notebook included in the NEST source code.

Remarks:

• All targets receive different currents.

• The currents for all targets change at the same points in time.

• The interval between changes, dt, must be a multiple of the time step.

• The effect of this noise current on a neuron depends on dt. Consider the membrane potential fluctuations evoked when a noise current is injected into a neuron. The standard deviation of these fluctuations across an ensemble will increase with dt for a given value of std. For the leaky integrate-and-fire neuron with time constant $$\tau_m$$ and capacity $$C_m$$, membrane potential fluctuations Sigma at time $$t_j+delay$$ are given by

$\begin{split}\Sigma = std * \tau_m / C_m * \sqrt( (1-x) / (1+x) ) \\ \text{where } x = exp(-dt/\tau_m)\end{split}$

for large $$t_j$$. In the white noise limit, $$dt \rightarrow 0$$, one has

$\Sigma \rightarrow std / C_m * \sqrt(dt * \tau / 2).$

To obtain comparable results for different values of dt, you must adapt std.

As the noise generator provides a different current for each of its targets, the current recorded represents the instantaneous average of all the currents computed. When there exists only a single target, this would be equivalent to the actual current provided to that target.

## Parameters¶

The following parameters can be set in the status dictionary:

 mean pA Mean value of the noise current std pA Standard deviation of noise current dt ms Interval between changes in current, default 1.0ms std_mod pA Modulated standard deviation of noise current phase real Phase of sine modulation (0-360 deg) frequency Hz Frequency of sine modulation

CurrentEvent